Related papers: Persistent Homology of Graph Embeddings

Transactional network data can be thought of as a list of one-to-many communications(e.g., email) between nodes in a social network. Most social network models convert this type of data into binary relations between pairs of nodes. We…

In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals…

The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…

Recently, persistent homology has had tremendous success in biomolecular data analysis. It works by examining the topological relationship or connectivity of a group of atoms in a molecule at a variety of scales, then rendering a family of…

Persistent homology is an effective method for extracting topological information, represented as persistent diagrams, of spatial structure data. Hence it is well-suited for the study of protein structures. Attempts to incorporate…

We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…

Spectral embedding of network adjacency matrices often produces node representations living approximately around low-dimensional submanifold structures. In particular, hidden substructure is expected to arise when the graph is generated…

Finding communities in networks is a problem that remains difficult, in spite of the amount of attention it has recently received. The Stochastic Block-Model (SBM) is a generative model for graphs with "communities" for which, because of…

Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…

Graph embeddings play a critical role in graph representation learning, allowing machine learning models to explore and interpret graph-structured data. However, existing methods often rely on opaque, high-dimensional embeddings, limiting…

Convection is a well-studied topic in fluid dynamics, yet it is less understood in the context of networks flows. Here, we incorporate techniques from topological data analysis (namely, persistent homology) to automate the detection and…

Link prediction is an important learning task for graph-structured data. In this paper, we propose a novel topological approach to characterize interactions between two nodes. Our topological feature, based on the extended persistent…

A very popular class of models for networks posits that each node is represented by a point in a continuous latent space, and that the probability of an edge between nodes is a decreasing function of the distance between them in this latent…

Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…

Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data…

Spectral clustering is a technique that clusters elements using the top few eigenvectors of their (possibly normalized) similarity matrix. The quality of spectral clustering is closely tied to the convergence properties of these principal…

For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…

We propose a framework to model the distribution of sequential data coming from a set of entities connected in a graph with a known topology. The method is based on a mixture of shared hidden Markov models (HMMs), which are jointly trained…

In this paper, we exploit the theory of dense graph limits to provide a new framework to study the stability of graph partitioning methods, which we call structural consistency. Both stability under perturbation as well as asymptotic…

Higher-order connectivity patterns such as small induced sub-graphs called graphlets (network motifs) are vital to understand the important components (modules/functional units) governing the configuration and behavior of complex networks.…